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2024 | OriginalPaper | Chapter

Structure of Cyclotomic Polynomials and Several Applications

Authors : Ala’a Al-Kateeb, Hoon Hong, Eunjeong Lee

Published in: Mathematical Analysis and Numerical Methods

Publisher: Springer Nature Singapore

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Abstract

The chapter delves into the intricate structure of cyclotomic polynomials, defined as the monic polynomials whose complex roots are the primitive n-th roots of unity. These polynomials play a fundamental role in number theory and algebra, with applications ranging from cryptography to computational efficiency. The author lists several interesting structures of cyclotomic polynomials, including relations among blocks obtained by suitable partitioning. Some of these structures are newly discovered, while others are explicitly stated and proven using a uniform technique. The chapter also illustrates the practical applications of these structural results, deriving properties such as the number of terms with prescribed coefficients, the norm of coefficients, and the coefficient of the middle term. These properties are shown to exhibit linear and parallel relationships, providing valuable insights into the behavior of cyclotomic polynomials.
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Metadata
Title
Structure of Cyclotomic Polynomials and Several Applications
Authors
Ala’a Al-Kateeb
Hoon Hong
Eunjeong Lee
Copyright Year
2024
Publisher
Springer Nature Singapore
Book
Mathematical Analysis and Numerical Methods

Print ISBN: 978-981-9748-75-4

Electronic ISBN: 978-981-9748-76-1

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-981-97-4876-1_14

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